Is the cricothyroid muscle the same muscle as the pharyngeal constrictors?

A University Student recently asked me,” Is the cricothyroid muscle part of the pharyngeal constrictors?”

My reply to the student was, “the cricothyroid muscle exists as an extension of the pharyngeal constrictors and is where the line of muscle merges.”

There is in fact a strong possibility that the cricothyroid muscle is a part of the pharyngeal constrictors. I realized this after I reviewed a video of the anatomy of the larynx, which I recorded at the Mayo Clinic. When I touched the cricothyroid muscle and the pharyngeal constrictors carefully, I noticed that both of those muscles seemed to be connected to each other.
I cannot say for sure, because although we live in modern times the science behind this area of muscle groups is still vague, in determining as well as knowing how the soft tissues are classified and move.

Note1:If the cricothyroid muscle is the same muscle as the pharyngeal constrictors, that means that the pharyngeal constrictors are also very important in controlling tone and pitch in vocalization.